Propensity
score matching and weighting are popular methods when estimating
causal effects in observational studies. Beyond the assumption of
unconfoundedness, however, these methods also require the model for
the propensity score to be correctly specified. The recently
proposed covariate balancing propensity score (CBPS) methodology
increases the robustness to model misspecification by directly
optimizing sample covariate balance between the treatment and
control groups. In this paper, we extend the CBPS to a continuous
treatment. We propose the covariate balancing generalized
propensity score (CBGPS) methodology, which minimizes the
association between covariates and the treatment. We develop both
parametric and nonparametric approaches and show their superior
performance over the standard maximum likelihood estimation in a
simulation study. The CBGPS methodology is applied to an
observational study, whose goal is to estimate the causal effects of
political advertisements on campaign contributions. We also provide
open-source
software that implements the proposed methods.